Geophysical Research Letters
  • Open Access

A wave roughness Reynolds number parameterization of the sea spray source flux


  • Sarah J. Norris,

    Corresponding author
    1. Institute of Climate and Atmospheric Science, School of Earth and Environment, University of Leeds, Leeds, UK
    • Corresponding author: S. J. Norris, Institute of Climate and Atmospheric Science, School of Earth and Environment, University of Leeds, Woodhouse Lane, Leeds LS2 9JT, UK. (

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  • Ian M. Brooks,

    1. Institute of Climate and Atmospheric Science, School of Earth and Environment, University of Leeds, Leeds, UK
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  • Dominic J. Salisbury

    1. Institute of Climate and Atmospheric Science, School of Earth and Environment, University of Leeds, Leeds, UK
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[1] Parameterizations of the sea spray aerosol source flux are derived as functions of wave roughness Reynolds numbers, RHa and RHw, for particles with radii between 0.176 and 6.61 µm at 80% relative humidity. These source functions account for up to twice the variance in the observations than does wind speed alone. This is the first such direct demonstration of the impact of wave state on the variability of sea spray aerosol production. Global European Centre for Medium-Range Weather Forecasts operational mode fields are used to drive the parameterizations. The source flux from the RH parameterizations varies from approximately 0.1 to 3 (RHa) and 5 (RHw) times that from a wind speed parameterization, derived from the same measurements, where the wave state is substantially underdeveloped or overdeveloped, respectively, compared to the equilibrium wave state at the local wind speed.

1 Introduction

[2] Sea spray aerosol (SSA) is a dominant contribution to the global atmospheric aerosol loading [Hoppel et al., 2002; Andreae and Rosenfeld, 2008]; it makes a significant contribution to the scattering of solar radiation, having a cooling influence on the Earth's surface (the aerosol direct effect [Intergovernmental Panel on Climate Change, 2007]) of up to 6 W m−2 [Lewis and Schwartz, 2004]. Highly hygroscopic, SSAs act as efficient cloud condensation nuclei [Andreae and Rosenfeld, 2008] and play an important role in determining the microphysical properties of marine clouds. As a sink for aerosol precursor gases, they act as a control on boundary layer nucleation processes [Merikanto et al., 2009]. Understanding the magnitude and variability of SSA production is essential to constraining estimates of preindustrial aerosol forcing of climate and estimating future climate, to accurately interpreting satellite data, and as a forcing term for global chemistry transport models and aerosol models.

[3] SSA is produced at the ocean surface by the bursting of bubbles generated primarily by breaking waves (radii of roughly 0.01–10 µm and 1–300 µm from film and jet drops, respectively) and the tearing of water droplets from wave crests (R > 200 µm) [Lewis and Schwartz, 2004]. Most parameterizations of SSA production (sea spray source functions) are specified either as simple functions of the mean wind speed [e.g., Smith et al., 1993; Hoppel et al., 2002] or as a production flux per unit area of whitecap scaled by the total surface whitecap fraction [e.g., Monahan et al., 1986; Mårtensson et al., 2003], which is in turn usually parameterized as a function of wind speed, most commonly using Monahan and O'Muircheartaigh [1980].

[4] In spite of decades of study, there remains an uncertainty of at least an order of magnitude in sea spray source functions [de Leeuw et al., 2011]. Wind speed alone cannot explain the observed variability in either SSA flux [de Leeuw et al., 2011] or whitecap fraction [Anguelova and Webster, 2006]. Water temperature and salinity [Mårtensson et al., 2003; Zabori et al., 2012] affect bubble properties via the viscosity and surface tension of water and the salt concentration in the droplets forming SSA. A larger source of variability is believed to result from the wave state [de Leeuw et al., 2011]; however, few studies of the SSA flux have made coincident, detailed measurements of wave properties.

[5] A joint measure of wind and wave state may be defined as a Reynolds number. Various formulations have been used to characterize wave breaking [Toba and Koga, 1986], whitecap fraction [Zhao and Toba, 2001; Goddijn-Murphy et al., 2011], and sea spray production [Zhao et al., 2006; Shi et al., 2009; Liu et al., 2012], although these last are all theoretical and do not provide evidence of a sea state dependence of the SSA flux. Here we use a wave Reynolds number RH introduced by Zhao and Toba [2001]:

display math(1)

where u* is the friction velocity, Hs is the significant wave height, and ν is a kinematic viscosity. Two variants were proposed: RHa defined using the viscosity of air, νa, and RHw using the viscosity of water νw. The latter was considered conceptually more robust for processes related to wave breaking and has since been used by Woolf [2005] and Goddijn-Murphy et al. [2011].

2 Measurements

[6] We use the direct eddy covariance SSA flux data set of Norris et al. [2012] and calculate the Reynolds numbers, RHa and RHw. All data were collected during cruise D317 of the RRS Discovery in the northeast Atlantic, from 21 March to 12 April 2007, as part of the Sea Spray, Gas Flux, and Whitecap (SEASAW) project, a UK contribution to the international Surface Ocean-Lower Atmosphere Study program [Brooks et al., 2009a]. Eddy covariance estimates of the SSA flux were made with a collocated sonic anemometer and Compact Lightweight Aerosol Spectrometer Probe (CLASP) [Hill et al., 2008]. The Reynolds numbers were calculated from in situ measurements. Hs was determined from measurements of the one-dimensional wave spectra by a MKIV shipborne wave recorder [Tucker and Pitt, 2001], while u* was measured via direct eddy covariance. νa and νw are calculated from measurements of air temperature and pressure using the Sutherland equation [Montgomery, 1947] and of water temperature and salinity [Sharqawy et al., 2010], respectively. Details of all instrumentation are given in Brooks et al. [2009b]. The turbulent flux calculations are described in Norris et al. [2012] and Sproson et al. [2013]. Norris et al. [2012] also discuss the mean meteorological and oceanographic conditions.

3 Results

[7] Sea spray source fluxes for individual CLASP size channels, adjusted to 80% relative humidity, are bin averaged by RHa and RHw and linear fits determined (see supporting information). Poor statistics in the two lowest RH bins results in unconstrained fits predicting a physically unrealistic positive SSA flux at RH = 0 for both the smallest and largest particles. Toba and Koga [1986] found a threshold of RB = 1000 for the onset of wave breaking, where inline image is the breaking wave Reynolds number and ωp is the peak angular frequency of the wind waves. Fitting measured RH to RB values, we find critical values of RHa = 7100 ± 2800 and RHw = (7.2 ± 2.9) × 104; both agree closely with the intercepts of RHa and RHw at zero flux obtained from unconstrained fits across the middle of the measured size range (see supporting information). Below these threshold values, we do not expect wave breaking to occur, and thus, the SSA flux should be zero; we thus force linear fits of the flux to RH through zero at these thresholds. The gradient, α, and intercept, β, of the linear fits are parameterized as functions of R80—the particle radius at 80% humidity—to define a SSA source function in terms of the Reynolds numbers:

display math(2)

[8] For RHa, we find

display math(3)

and for RHw

display math(4)

[9] No assumptions were made about the functional forms; these were chosen purely on the grounds of the best fit to the data. The R2 values for the fits against both RHa and RHw are shown in Figure 1 along with those for the fits against the 10 m wind speed, U10, from Norris et al. [2012]. The Reynolds numbers explain much more of the observed variability in the source flux than does U10 alone over most of the measured size range—by 20–60% between 1 and 4 µm, and almost a factor of 2 for RHw at 5 µm; however, R2 decreases substantially for the smallest and largest size channels where the small number of data points available results in a large uncertainty. RHw does slightly better than RHa, increasingly so as particle size increases. Their formulations differ only in the viscosity used; these have very narrow ranges (1.36–1.42 × 10−5 m2 s−1 for νa, 1.32–1.45 × 10−6 m2 s−1 for νw) compared to those of u* (0.11–0.80 m s−1) and Hs (1.91–5.08 m) within the SEASAW data set. This results from narrow temperature ranges for air (4.7–12.0°C) and water (8.8–12.1°C) (see supporting information). If the points with poor counting statistics are excluded from the analysis, the R2 values increase substantially (Figure 1), though they still drop off rapidly for R80 > 5 µm.

Figure 1.

The R2 values for the fits of the observed source flux to U10 (black), both RHa (red triangle) and RHw (blue inverted triangle) with fits forced through RHa = 7100 and RHw = 7.2 × 104, and unconstrained (pink and pale blue). For those channels affected by poor counting statistics in the two lowest Reynolds number bins, R2 is also shown after removing those points (plus sign).

[10] The new parameterization (4) is compared with several existing functions in Figure 2 (the alternative parameterization (3) (not shown) gives near-identical results). Because most of these functions depend on wind speed only, we evaluate (4) at the mean RHw observed over the specified wind speed range during SEASAW and show an uncertainty range corresponding to the range of RHw. We include the source function of Liu et al. [2012] formulated in terms of RB to combine the whitecap function of Zhao and Toba [2001] and sea spray source function of Monahan [1986]. Again, this function is evaluated for mean and limiting values of RB within the wind speed bin.

Figure 2.

The RHw-dependent source function from (4) compared with a number of recent functions at U10 = 10 m s−1. Parameterization (4) is plotted for the mean observed value of RHw for 9.5 < U10 < 10.5 m s−1. Three different sources of uncertainty are shown: the pick shaded region indicates the range of fluxes resulting from the range of observed RHw (4.5 × 105 < RHw < 9.5 × 105); the red dashed lines indicate the 95% confidence intervals in the best fit to α and β, and the red dash-dotted line indicates the uncertainty associated with the 95% confidence intervals on the fits of the raw flux estimates to RHw. The pale green area indicates the uncertainty in Liu et al. [2012] resulting from the observed range of RB values within the wind speed range. The pale blue area is the published uncertainty in the Lewis and Schwartz [2004] parameterization. Thin black dashed lines indicate the uncertainty in the Norris et al. [2012] function.

[11] In order to evaluate the potential impact of accounting for wave state on the SSA source flux, we calculate the flux from both the U10-dependent function of Norris et al. [2012] and (3) and (4) using the European Centre for Medium-Range Weather Forecasts (ECMWF) operational mode global fields for 0000 UTC 1 January 2011. U10 and Hs are taken directly from the model, while u* is calculated from U10 and the wave model's sea state-dependent drag coefficient [Janssen, 2000]. Salinity is taken from the 2009 World Ocean Atlas [Antonov et al., 2010]. The ratio between the source fluxes from (3) and (4) and Norris et al. [2012] is shown in Figure 3 for R80 = 0.5 µm. Also shown are fields of U10, the Norris et al. [2012] source flux, RHa, RHw, Hs, and the ratio Hs/Hfd where Hfd is the value of Hs for waves in equilibrium with the local wind, calculated from the WAM model wind-wave relation [Wave Model Development and Implementation Group, 1988]; Hs/Hfd gives a measure of the degree of wave development. In order to avoid any bias that might result from extrapolating the source functions beyond the range of conditions from which they were derived, we have excluded grid points with winds outside the observed range of 4 < U10 < 18 m s−1.

Figure 3.

Global distributions of (a) wind speed, U10; (b) SSA flux from Norris et al. [2012]; (c) significant wave height, Hs; (d) Hs/Hfd; (e) RHa; (f) RHw; (g) ratio of sea spray source flux dF/dR80 from the RHa (3) and U10 [Norris et al., 2012] parameterizations at R80 = 0.5 µm; and (h) same as Figure 3g but for RHw. Example regions where the Reynolds number function is significantly higher/lower than the U10 function are indicated by purple/brown boxes.

[12] There are some substantial differences between the parameterizations; the RHa parameterization ranges from less than 0.1 of the U10 source function to about 3 times larger; the RHw function peaks at 5 times larger. A comparison of the spatial distribution of the differences to those of the forcing parameters is revealing. Consider first the RHa function (Figure 3g). The regions where its ratio with the U10 function is largest coincide not with the highest winds or Reynolds numbers in storm systems, but around the margins of these systems. These are regions where the wavefield is significantly better developed than the equilibrium wavefield for the local wind (Hs/Hfd > 1); two such regions are indicated by purple boxes. In regions where the wave state is underdeveloped compared to the equilibrium state—notably in the regions of highest wind speed within storm systems—the RHa parameterization falls below the U10 parameterization; examples are indicated by the brown boxes. The RHw parameterization follows a similar spatial pattern but predicts somewhat higher fluxes over the tropical and subtropical oceans. This is a consequence of the stronger temperature dependence of water viscosity compared to that of air. The implications of this and the limitations it imposes on the interpretation of our results are discussed below.

4 Conclusions

[13] New parameterizations of the sea spray source flux (0.176 < R80 < 6.61 µm) have been derived as functions of wave Reynolds numbers, RHa and RHw. They account for up to twice the variance in the measured fluxes than does wind speed alone. The variance explained decreases with particle size for all three parameterizations; at the smallest sizes, U10 and RH account for similar variance, and that explained by U10 then falls more rapidly with particle size than that for RHa and RHw. The size dependence of R2 is consistent with Norris et al. [2013] who found that SSA production per unit area whitecap was wind speed dependent for R80 < 2 µm, but showed no clear relationship at larger sizes. We speculate that this behavior is related to changes in bubble populations with increasing wind and wave breaking—Norris et al. [2013] found that concentrations of small bubbles increased more than those of large bubbles with increasing wind speed—and the sizes of aerosol particles generated by different-sized bubbles. Here, jet drops will dominate production for R80 > 1 µm and film drops for R80 < 1 µm.

[14] A comparison of the ratio of the new parameterizations to the wind speed-dependent function derived by Norris et al. [2012] from the same data set shows differences of a factor of 0.1 to 3 (RHa) and 5 (RHw). Fluxes higher than those of the U10 function are found around the margins of storm systems where propagation of waves away from the regions of highest winds results in wave states that are overdeveloped compared to the equilibrium state for the local wind. Fluxes lower than those from the U10 function are found where the wave state is underdeveloped. We emphasize that both the U10 and RH-dependent source functions are derived from the same in situ measurements; differences between them arise almost entirely from the inclusion of information on wave state via the Reynolds number. Superficially, the results appear contrary to those of Norris et al. [2012] that the flux was higher in undeveloped seas for a given wind speed. In fact, there is no direct contradiction. Norris et al. [2012] characterized wave development by the mean wave slope; this depends only on Hs and Tz, the zero-crossing period of the waves, and says nothing about the relationship between the observed waves and those expected under equilibrium with the local wind.

[15] The RHw function predicts larger fluxes than RHa over much of the ocean—a result of the stronger temperature dependence of viscosity for water than for air. The observations used to derive the source functions span a limited range of temperatures. This leaves open the possibility that viscosity-dependent properties of wave breaking or bubbles might affect the SSA flux in a manner not accounted for by these source functions. Measurements under a much wider range of conditions are required to address this issue. The data set is also not large enough to assess any separate impact of wind waves and swell, nor of relative wind and wave directions, both of which may complicate the wind-wave-flux relationship [e.g., Goddijn-Murphy et al., 2011]. Thus, the source functions proposed cannot be considered universal but are a significant step toward this goal and an improvement on simple wind speed-dependent functions.

[16] At any given time, the wave state over the majority of the world's oceans is out of equilibrium with the local wind—the majority being overdeveloped and dominated by swell; just 8.5% is found to be underdeveloped in the ECMWF fields by the Wave Model Development and Implementation definition. Simple wind speed-dependent SSA source functions will tend to misrepresent the spatial variability of SSA production. This has implications for modeling of new particle formation and regional aerosol budgets, marine atmospheric boundary layer chemistry, and the spatial variability of cloud condensation nuclei concentrations over the oceans. The new parameterizations are readily implemented in models and should lead to better representation of the spatial and temporal variability of sea spray fluxes.


[17] This work was funded by the UK Natural Environment Research Council grants NE/C001842/1 as part of UK SOLAS, NE/G00353X/1, and NE/G000107/1. We thank the Captain and crew of the RRS Discovery and the staff of National Marine Facilities Sea Systems for their assistance in preparing for and during the cruise, ECMWF for the global model reanalysis fields, and David Woolf and an anonymous reviewer for their constructive comments on the manuscript.

[18] The Editor thanks David Woolf and an anonymous reviewer for their assistance in evaluating this paper.